# Exponential Problem Solving

Remember that exponential functions are named that because of the “\(x\)” in their exponents! “\(b\)” is called the base of the exponential function, since it’s the number that is multiplied by itself “\(x\)” times (and it’s not an exponential function when \(b=1\)).\(b\) is also called the “growth” or “decay” factor.Exponential functions often involve the rate of increase or decrease of something.

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Also note that Factoring with Exponents and Solving Exponential Equations after Factoring can be found in the Advanced Factoring section here.

And when we study Geometric Sequences, we’ll see that they are a discrete form of an exponential function.

The formula for compound interest with a finite number of calculations is an exponential equation.

We can solve for a parameter of this equation, and can use logarithms to access parameters in the exponent.

Our goal will be to rewrite both sides of the equation so that the base is the same.

Unlike bases often involve negative or fractional bases like the example below.

Students may be asked to solve compound interest problems with interest compounded biannually, monthly, or daily.

If something increases at a constant rate, you may have exponential growth on your hands.

Examples, videos, worksheets, and activities to help Pre Calculus students learn how to apply exponential functions.

Compound Interest (Finite Number of Calculations) One real world application of exponential equations is in compound interest.

• ###### Exponential and Logarithmic Equations College Algebra

Do all exponential equations have a solution? If not, how can we tell if there is a solution during the problem-solving process? No. Recall that the range of an exponential function is always positive. While solving the equation we may obtain an expression that is undefined.…

• ###### Solving Exponential Equations - Cool Math

Solving Exponential Equations. We HAVE to solve for Mr. t. I pity the fool who can't solve Mr. t! Pity the fool! Sorry for the lame A-Team joke.…

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Solving Exponential Equations. Solving for Time and Rates. More Ways to Use This Stuff. Tricks to Help with Solving Log Equations. Solving Log Equations. Exercises…

• ###### Solving Exponential and Logarithmic Equations

Solve exponential equations. Solve logarithmic equations. Solve exponential and logarithmic inequalities. Solving Exponential Equations Exponential equations are equations in which variable expressions occur as exponents. The result below is useful for solving certain exponential equations. The preceding property is useful for solving an.…

• ###### Exponential Functions and Sequences - rchs.

Chapter 6 Exponential Functions and Sequences Mathematical Practices Problem-Solving Strategies Mathematically profi cient students look closely to fi nd a pattern. Monitoring Progress 1. A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. Find the population in the tenth year. 2.…

• ###### Examples of Solving Logarithmic Equations

Rewrite the problem in exponential form by moving the base of the logarithm to the other side. Simplify the problem by distributing and squaring the 6. Solve the problem by subtracting 36 from each side to ge t it equal to zero, and then factoring or using the quadratic formula to find the values of x.…

• ###### Working with Exponents and Logarithms - Math Is Fun

Working with Exponents and Logarithms. Always try to use Natural Logarithms and the Natural Exponential Function whenever possible. Solve 2 log 8 x = log 8 16.…

• ###### Exp & Log Problem Solving - PreCalculus

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